conv_observed_order — CONVERGE `verification` op

• 資料種類:無 → table(僅由參數決定的運算子 —— 不接受影像或資料輸入)

• 呼叫: import fullseye as fs; fs.ledger.conv_observed_order(phi=None, h=None, r=None, n_cells=None, dim=None) -> 'dict'(要直接呼叫實作,import converge; converge.conv_observed_order(phi=None, h=None, r=None, n_cells=None, dim=None) -> 'dict';從台帳取用則 opsconverge.get("conv_observed_order"))

用法

由三個系統加密的解求表觀收斂階 p（Celik 等 2008，式 3）。

> 以下的詳細說明為原文 —— 摘要與標題已翻譯。

phi = (phi1, phi2, phi3) on grids 1 (finest) .. 3 (coarsest). The refinement is given by exactly one of h = (h1, h2, h3) representative cell sizes, r = (r21, r32) with r21 = h2/h1 and r32 = h3/h2, or n_cells = (N1, N2, N3) with dim (h from Celik eqs. (1)-(2)). With eps32 = phi3 - phi2 and eps21 = phi2 - phi1 (Step 3):

p = |ln|eps32/eps21| + q(p)| / ln(r21) (3a)

q(p) = ln((r21^p - s) / (r32^p - s)) (3b)

s = sign(eps32 / eps21) (3c)

solved by fixed-point iteration from the first term (q = 0) with iterate_fixed_point (plain, as the paper prescribes; |p_k+1 - p_k| <= 1e-13, at most 1000 steps). q = 0 when r is constant. s = -1 flags oscillatory convergence (reported, not refused — Celik keeps the absolute values so the extrapolation goes toward h = 0).

Refusal: eps21 or eps32 "very close" to zero (|eps| <= 1e-12 * max|phi|) — Celik: the procedure does not work there (oscillation or an exact solution; refine further) — and a fixed-point iteration for p that does not converge.

Defaults: the first column of Celik et al. 2008 Table 1 (p = 1.53).

詳細使用指南

• convergent_computation 族使用指南

參考(範例資料、文獻)

• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。

• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。

• 演算法的正典(作者、年份)與用途見上面的族使用指南。

可執行的範例(實際呼叫該運算子並已驗證的樣例)

• (尚無)

型別可銜接的下一個運算子(可接受 `table` 作為輸入)

—

同類別(`verification`)

conv_gci

*Provenance: converge.py — CONVERGE 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*

conv_observed_order — CONVERGE verification op

用法